where \(T(X_{i,0}^-;\theta )=X_i^-\)  represents a shortrun Langevin trajectory with the EBM \(p(x;\theta )\) . This loss can be derived in the ML framework as a way to teach the output of \(g(z ;\phi )\)  to match the distribution of \(p(x;\theta )\) . A full implementation of cooperative learning requires an additional sampling process on \(Z_i\) , but we use a straight-through estimator [1]} and approximate latent sampling with the identity function as originally done in the official MATLAB implementation from [2]}. We review further details of the cooperative learning loss in Appendix REF .
